Analysis for SSFA project: Three factor model

Filtered weakly by < 20% NMP

Table of contents

1. Used packages
2. Global settings
3. Load data
4. Explore data
5. Model specification
6. Inference
   1. epLsar
   2. R²
   3. Asfc
   4. Smfc
   5. HAsfc9
7. Summary

Used packages

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns; sns.set()
import pickle
import arviz as az
import pymc3 as pm

from matplotlib.colors import to_rgb

import scipy.stats as stats 

from IPython.display import display

import matplotlib as mpl

%load_ext autoreload
%autoreload 2

import plotting_lib

Global settings

Output

writeOut = True
outPathPlots = "../plots/statistical_model_three_factors_filter_weak/"
outPathData = "../derived_data/statistical_model_three_factors_filter_weak/"

Plotting

widthMM = 190 
widthInch = widthMM / 25.4
ratio = 0.66666
heigthInch = ratio*widthInch

SMALL_SIZE = 8
MEDIUM_SIZE = 10
BIGGER_SIZE = 12

plt.rc('font', size=SMALL_SIZE)          # controls default text sizes
plt.rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title
plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels
plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels
plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels
plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize
plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title
sns.set_style("ticks")

dpi = 300

sizes = [SMALL_SIZE,MEDIUM_SIZE,BIGGER_SIZE]

Computing

numSamples = 1000
numCores = 4
numTune = 1000
numPredSamples = 2000
random_seed=36514535
target_accept = 0.99

Load data

datafile = "../derived_data/preprocessing/preprocessed_filter_weak.dat"

with open(datafile, "rb") as f:
    x1,x2,x3,df,dataZ,dictMeanStd,dictTreatment,dictSoftware = pickle.load(f)    

Show that everything is correct:

display(pd.DataFrame.from_dict({'x1':x1,'x2':x2,'x3':x3}))

	x1	x2	x3
0	0	5	115
1	1	5	115
2	0	5	116
3	1	5	116
4	0	5	117
...	...	...	...
273	1	9	52
274	0	9	53
275	1	9	53
276	0	9	54
277	1	9	54

278 rows × 3 columns

x1 indicates the software used, x2 indicates the treatment applied and x3 the sample.

for surfaceParam,(mean,std) in dictMeanStd.items():
    print("Surface parameter {} has mean {} and standard deviation {}".format(surfaceParam,mean,std))

Surface parameter epLsar has mean 0.0032388209205305753 and standard deviation 0.0019378273835719989
Surface parameter Rsquared has mean 0.9974096825435252 and standard deviation 0.007283582118542012
Surface parameter Asfc has mean 14.919474245449283 and standard deviation 12.47068676838922
Surface parameter Smfc has mean 1.155270960424856 and standard deviation 7.13503174525663
Surface parameter HAsfc9 has mean 0.44593694325514915 and standard deviation 0.7912033512620836
Surface parameter HAsfc81 has mean 0.9300206156734742 and standard deviation 2.3638534390774013

for k,v in sorted(dictTreatment.items(), key=lambda x: x[0]):    
    print("Number {} encodes treatment {}".format(k,v))

Number 0 encodes treatment BrushDirt
Number 1 encodes treatment BrushNoDirt
Number 2 encodes treatment Clover
Number 3 encodes treatment Clover+dust
Number 4 encodes treatment Control
Number 5 encodes treatment Dry bamboo
Number 6 encodes treatment Dry grass
Number 7 encodes treatment Dry lucerne
Number 8 encodes treatment Grass
Number 9 encodes treatment Grass+dust
Number 10 encodes treatment RubDirt

for k,v in dictSoftware.items():
    print("Number {} encodes software {}".format(k,v))

Number 0 encodes software ConfoMap
Number 1 encodes software Toothfrax

display(dataZ)

	index	TreatmentNumber	SoftwareNumber	DatasetNumber	NameNumber	epLsar_z	Rsquared_z	Asfc_z	Smfc_z	HAsfc9_z	HAsfc81_z
0	0	5	0	0	115	0.608031	0.081494	-0.261684	-0.120632	-0.391977	-0.239736
1	1	5	1	0	115	0.764866	0.295228	-0.368764	-0.145206	-0.392397	-0.240365
2	2	5	0	0	116	1.355641	-0.166422	0.043912	-0.120632	-0.346351	-0.268091
3	3	5	1	0	116	1.350574	0.282460	-0.137943	-0.145206	-0.349727	-0.282929
4	4	5	0	0	117	0.930308	-0.359987	-0.137793	-0.120632	-0.233444	-0.221925
...	...	...	...	...	...	...	...	...	...	...	...
273	273	9	1	2	52	0.611602	0.267769	-1.050437	0.035516	0.493708	0.076860
274	274	9	0	2	53	0.084569	0.197735	-0.966638	-0.093723	0.242115	0.257597
275	275	9	1	2	53	-0.051512	0.319804	-0.975181	-0.143224	0.644288	0.381453
276	276	9	0	2	54	-1.041990	0.284041	-1.077552	0.011489	-0.095103	-0.053253
277	277	9	1	2	54	-1.308590	0.336005	-1.081522	-0.104672	-0.126169	-0.038105

278 rows × 11 columns

display(df)

	Dataset	Name	Software	Diet	Treatment	Before.after	NMP	NMP_cat	epLsar	Rsquared	Asfc	Smfc	HAsfc9	HAsfc81	NewEplsar	TreatmentNumber	SoftwareNumber	DatasetNumber	NameNumber
0	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_1	ConfoMap	Dry bamboo	Dry bamboo	NaN	0.717312	0-5%	0.004417	0.998003	11.656095	0.294557	0.135803	0.363319	0.019460	5	0	0	115
1	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_1	Toothfrax	Dry bamboo	Dry bamboo	NaN	0.717312	0-5%	0.004721	0.999560	10.320730	0.119219	0.135471	0.361833	NaN	5	1	0	115
2	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_2	ConfoMap	Dry bamboo	Dry bamboo	NaN	1.674215	0-5%	0.005866	0.996198	15.467083	0.294557	0.171903	0.296292	0.020079	5	0	0	116
3	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_2	Toothfrax	Dry bamboo	Dry bamboo	NaN	1.674215	0-5%	0.005856	0.999467	13.199232	0.119219	0.169232	0.261217	NaN	5	1	0	116
4	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_3	ConfoMap	Dry bamboo	Dry bamboo	NaN	1.760409	0-5%	0.005042	0.994788	13.201101	0.294557	0.261235	0.405422	0.019722	5	0	0	117
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
273	Sheeps	L8-Ovis-90730-lm2sin-a	Toothfrax	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.004424	0.999360	1.819802	1.408678	0.836560	1.111706	NaN	9	1	2	52
274	Sheeps	L8-Ovis-90764-lm2sin-a	ConfoMap	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.003403	0.998850	2.864831	0.486556	0.637499	1.538943	0.018978	9	0	2	53
275	Sheeps	L8-Ovis-90764-lm2sin-a	Toothfrax	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.003139	0.999739	2.758297	0.133366	0.955699	1.831721	NaN	9	1	2	53
276	Sheeps	L8-Ovis-90814-lm2sin-a	ConfoMap	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.001220	0.999479	1.481662	1.237247	0.370691	0.804138	0.017498	9	0	2	54
277	Sheeps	L8-Ovis-90814-lm2sin-a	Toothfrax	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.000703	0.999857	1.432148	0.408433	0.346111	0.839946	NaN	9	1	2	54

278 rows × 19 columns

Contrasts

Prepare dicts for contrasts that are of interest later.

x1contrast_dict = {'{}_{}'.format(dictSoftware[0],dictSoftware[1]):[1,-1]}
x1contrast_dict

{'ConfoMap_Toothfrax': [1, -1]}

Explore data

Compute raw differences

dfRawDiff = dataZ.groupby(['DatasetNumber','TreatmentNumber','NameNumber']).agg(list).applymap(lambda l : l[0]-l[1]).reset_index()

dfRawDiff

	DatasetNumber	TreatmentNumber	NameNumber	index	SoftwareNumber	epLsar_z	Rsquared_z	Asfc_z	Smfc_z	HAsfc9_z	HAsfc81_z
0	0	5	115	-1	-1	-0.156835	-0.213734	0.107080	0.024574	0.000420	0.000629
1	0	5	116	-1	-1	0.005067	-0.448881	0.181855	0.024574	0.003376	0.014838
2	0	5	117	-1	-1	0.137060	-0.615262	0.171673	0.024574	0.055406	0.020671
3	0	5	118	-1	-1	0.363489	-0.380505	0.206489	0.029593	0.018505	-0.035897
4	0	5	119	-1	-1	0.135927	-0.441161	0.431840	0.029593	0.051468	0.035179
...	...	...	...	...	...	...	...	...	...	...	...
134	2	9	50	-1	-1	0.565233	-0.166711	0.141982	0.016303	0.055662	0.046721
135	2	9	51	-1	-1	1.694319	-0.156497	0.021729	0.016303	0.446416	0.141461
136	2	9	52	-1	-1	-2.109816	-0.348137	0.000667	0.390193	-0.010465	0.004987
137	2	9	53	-1	-1	0.136080	-0.122069	0.008543	0.049501	-0.402172	-0.123856
138	2	9	54	-1	-1	0.266600	-0.051963	0.003970	0.116161	0.031066	-0.015148

139 rows × 11 columns

Show difference between software in raw data

variablesList = ['epLsar','Rsquared','Asfc','Smfc','HAsfc9']

for var in variablesList:
    fig, axes = plt.subplots(1, 2,figsize=(12,6))
    fig.suptitle('{}'.format(var))

    
    sns.stripplot(data=dataZ,x='NameNumber',y='{}_z'.format(var),hue='SoftwareNumber',ax=axes[0]);
    axes[0].set_title('Raw data')

    sns.histplot(data=dfRawDiff,x='{}_z'.format(var),ax=axes[1]);
    axes[1].set_title('Aggegrated difference by software'.format(var))

    plt.show()

Model specification

class ThreeFactorModel(pm.Model):
    
    """
    Compute params of priors and hyperpriors.
    """
    def getParams(self,x1,x2,x3,y):
        # get lengths
        Nx1Lvl = np.unique(x1).size
        Nx2Lvl = np.unique(x2).size
        Nx3Lvl = np.unique(x3).size        
        
        dims = (Nx1Lvl, Nx2Lvl, Nx3Lvl)
        
        ### get standard deviations
        
        # convert to pandas dataframe to use their logic
        df = pd.DataFrame.from_dict({'x1':x1,'x2':x2,'x3':x3,'y':y})
        
        s1 = df.groupby('x1').std()['y'].max()
        s2 = df.groupby('x2').std()['y'].max()
        s3 = df.groupby('x3').std()['y'].max()
        
        stdSingle = (s1, s2, s3)
        
        return (dims, stdSingle)
    
    def printParams(self,x1,x2,x3,y):
        dims, stdSingle = self.getParams(x1,x2,x3,y)
        Nx1Lvl, Nx2Lvl, Nx3Lvl = dims
        s1, s2, s3 = stdSingle        
        
        print("The number of levels of the x variables are {}".format(dims))
        print("The standard deviations used for the beta priors are {}".format(stdSingle))
            
    def __init__(self,name,x1,x2,x3,y,model=None):
        
        # call super's init first, passing model and name
        super().__init__(name, model)
        
        # get parameter of hyperpriors
        dims, stdSingle = self.getParams(x1,x2,x3,y)
        Nx1Lvl, Nx2Lvl, Nx3Lvl = dims
        s1, s2, s3 = stdSingle        
        
        ### hyperpriors ### 
        # observation hyperpriors
        lamY = 1/30.
        muGamma = 0.5
        sigmaGamma = 2.
        
        # prediction hyperpriors
        sigma0 = pm.HalfNormal('sigma0',sd=1)
        sigma1 = pm.HalfNormal('sigma1',sd=s1, shape=Nx1Lvl)
        sigma2 = pm.HalfNormal('sigma2',sd=s2, shape=Nx2Lvl)
        sigma3 = pm.HalfNormal('sigma3',sd=s3, shape=Nx3Lvl)
                
        mu_b0 = pm.Normal('mu_b0', mu=0., sd=1)
        mu_b1 = pm.Normal('mu_b1', mu=0., sd=1, shape=Nx1Lvl)
        mu_b2 = pm.Normal('mu_b2', mu=0., sd=1, shape=Nx2Lvl)
        mu_b3 = pm.Normal('mu_b3', mu=0., sd=1, shape=Nx3Lvl)       
                                       
        ### priors ### 
        # observation priors        
        nuY = pm.Exponential('nuY',lam=lamY)
        sigmaY = pm.Gamma('sigmaY',mu=muGamma, sigma=sigmaGamma)
        
        # prediction priors
        b0_dist = pm.Normal('b0_dist', mu=0, sd=1)
        b0 = pm.Deterministic("b0", mu_b0 + b0_dist * sigma0)
       
        b1_dist = pm.Normal('b1_dist', mu=0, sd=1)
        b1 = pm.Deterministic("b1", mu_b1 + b1_dist * sigma1)
        
        b2_dist = pm.Normal('b2_dist', mu=0, sd=1)
        b2 = pm.Deterministic("b2", mu_b2 + b2_dist * sigma2)
        
        b3_dist = pm.Normal('b3_dist', mu=0, sd=1)
        b3 = pm.Deterministic("b3", mu_b3 + b3_dist * sigma3)
             
        #### prediction ###      
        mu = pm.Deterministic('mu',b0 + b1[x1] + b2[x2] +  b3[x3])

                                
        ### observation ### 
        y = pm.StudentT('y',nu = nuY, mu=mu, sd=sigmaY, observed=y)

Inference

epLsar

with pm.Model() as model:
    epLsarModel = ThreeFactorModel('epLsar',x1,x2,x3,dataZ.epLsar_z.values)

Verify model settings

epLsarModel.printParams(x1,x2,x3,dataZ.epLsar_z.values)

The number of levels of the x variables are (2, 11, 139)
The standard deviations used for the beta priors are (1.0181033807478441, 1.4891257020651163, 1.4918655146500768)

try:
    graph_epLsar = pm.model_to_graphviz(epLsarModel)    
except:
    graph_epLsar = "Could not make graph"
graph_epLsar

Check prior choice

with epLsarModel as model:
    prior_pred_epLsar = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_epLsar,dataZ.epLsar_z.values,'epLsar')

Prior choice is as intended: Broad over the data range.

Sampling

with epLsarModel as model:
    trace_epLsar = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=target_accept,random_seed=random_seed)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [epLsar_b3_dist, epLsar_b2_dist, epLsar_b1_dist, epLsar_b0_dist, epLsar_sigmaY, epLsar_nuY, epLsar_mu_b3, epLsar_mu_b2, epLsar_mu_b1, epLsar_mu_b0, epLsar_sigma3, epLsar_sigma2, epLsar_sigma1, epLsar_sigma0]

100.00% [8000/8000 09:48<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 590 seconds.
The estimated number of effective samples is smaller than 200 for some parameters.

with epLsarModel as model:
    if writeOut:
        with open(outPathData + 'model_{}.pkl'.format('epLsar'), 'wb') as buff:
            pickle.dump({'model':epLsarModel, 'trace': trace_epLsar}, buff)

Check sampling

with epLsarModel as model:
    dataTrace_epLsar = az.from_pymc3(trace=trace_epLsar)

pm.summary(dataTrace_epLsar,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
epLsar_mu_b0	-0.04	0.79	-1.50	1.64	0.01	0.01	4578.0	2208.0	4588.0	3218.0	1.00
epLsar_mu_b1[0]	0.02	0.68	-1.42	1.25	0.01	0.01	3638.0	2339.0	3636.0	3182.0	1.00
epLsar_mu_b1[1]	-0.04	0.68	-1.41	1.22	0.01	0.01	3590.0	2011.0	3596.0	2887.0	1.00
epLsar_mu_b2[0]	-0.14	0.53	-1.16	0.89	0.01	0.01	1993.0	1993.0	1996.0	2449.0	1.00
epLsar_mu_b2[1]	-0.18	0.52	-1.22	0.81	0.01	0.01	1963.0	1825.0	1958.0	2574.0	1.00
...	...	...	...	...	...	...	...	...	...	...	...
epLsar_mu[273]	0.18	0.78	-1.65	0.90	0.05	0.03	283.0	283.0	555.0	965.0	1.01
epLsar_mu[274]	0.05	0.11	-0.17	0.26	0.00	0.00	4555.0	2784.0	4392.0	3415.0	1.00
epLsar_mu[275]	-0.01	0.11	-0.22	0.22	0.00	0.00	4624.0	2478.0	4478.0	3058.0	1.00
epLsar_mu[276]	-1.11	0.14	-1.38	-0.87	0.00	0.00	4435.0	4420.0	4210.0	3317.0	1.00
epLsar_mu[277]	-1.18	0.14	-1.43	-0.92	0.00	0.00	4418.0	4415.0	4205.0	3404.0	1.00

743 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_epLsar,dataTrace_epLsar,'epLsar')

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with epLsarModel as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_epLsar,'epLsar')

with epLsarModel as model:
    plotting_lib.pm.energyplot(trace_epLsar)

Posterior predictive distribution

with epLsarModel as model:
    posterior_pred_epLsar = pm.sample_posterior_predictive(trace_epLsar,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_epLsar,posterior_pred_epLsar,dataZ.epLsar_z.values,'epLsar')

Compare prior and posterior for model parameters

with epLsarModel as model:
    pm_data_epLsar = az.from_pymc3(trace=trace_epLsar,prior=prior_pred_epLsar,posterior_predictive=posterior_pred_epLsar)

arviz.data.io_pymc3 - WARNING - posterior predictive variable epLsar_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,pm_data_epLsar,'epLsar')

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_epLsar,'epLsar')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_epLsar,'epLsar')

Rsquared

with pm.Model() as model:
    RsquaredModel = ThreeFactorModel('Rsquared',x1,x2,x3,dataZ["Rsquared_z"].values)

Verify model settings

RsquaredModel.printParams(x1,x2,x3,dataZ["Rsquared_z"].values)

The number of levels of the x variables are (2, 11, 139)
The standard deviations used for the beta priors are (1.364226512794052, 3.833663350609328, 8.30397573287845)

pm.model_to_graphviz(RsquaredModel)

Check prior choice

with RsquaredModel as model:
    prior_pred_Rsquared = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_Rsquared,dataZ["Rsquared_z"].values,'Rsquared')

Sampling

with RsquaredModel as model:
    trace_Rsquared = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=target_accept,random_seed=random_seed)
    #fit_Rsquared = pm.fit(random_seed=random_seed)
    #trace_Rsquared = fit_Rsquared.sample(draws=numSamples)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Rsquared_b3_dist, Rsquared_b2_dist, Rsquared_b1_dist, Rsquared_b0_dist, Rsquared_sigmaY, Rsquared_nuY, Rsquared_mu_b3, Rsquared_mu_b2, Rsquared_mu_b1, Rsquared_mu_b0, Rsquared_sigma3, Rsquared_sigma2, Rsquared_sigma1, Rsquared_sigma0]

100.00% [8000/8000 13:46<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 827 seconds.
The estimated number of effective samples is smaller than 200 for some parameters.

with RsquaredModel as model:
    if writeOut:
        with open(outPathData + 'model_{}.pkl'.format('Rsquared'), 'wb') as buff:
            pickle.dump({'model': RsquaredModel, 'trace': trace_Rsquared}, buff)

Check sampling

with RsquaredModel as model:
    dataTrace_Rsquared = az.from_pymc3(trace=trace_Rsquared)

pm.summary(dataTrace_Rsquared,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
Rsquared_mu_b0	0.05	0.82	-1.58	1.64	0.01	0.01	3512.0	2594.0	3532.0	3278.0	1.0
Rsquared_mu_b1[0]	-0.08	0.73	-1.44	1.38	0.01	0.01	2577.0	2577.0	2580.0	2991.0	1.0
Rsquared_mu_b1[1]	0.11	0.73	-1.31	1.57	0.01	0.01	2693.0	2356.0	2682.0	2826.0	1.0
Rsquared_mu_b2[0]	0.08	0.53	-0.98	1.16	0.01	0.01	1410.0	1410.0	1396.0	1961.0	1.0
Rsquared_mu_b2[1]	-0.11	0.51	-1.04	0.98	0.02	0.01	1221.0	1221.0	1228.0	1654.0	1.0
...	...	...	...	...	...	...	...	...	...	...	...
Rsquared_mu[273]	0.21	0.09	0.05	0.40	0.00	0.00	4436.0	3566.0	4200.0	3064.0	1.0
Rsquared_mu[274]	0.14	0.09	-0.05	0.31	0.00	0.00	4024.0	2720.0	4023.0	2677.0	1.0
Rsquared_mu[275]	0.38	0.09	0.20	0.56	0.00	0.00	4009.0	3705.0	3956.0	2511.0	1.0
Rsquared_mu[276]	0.19	0.11	-0.01	0.41	0.00	0.00	4329.0	2580.0	4159.0	3037.0	1.0
Rsquared_mu[277]	0.43	0.11	0.22	0.64	0.00	0.00	4296.0	3506.0	4111.0	2970.0	1.0

743 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,dataTrace_Rsquared,trace_Rsquared,'Rsquared')

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.
  FutureWarning,
/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.
  FutureWarning,
/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,
/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.
  FutureWarning,
/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.
  FutureWarning,

with RsquaredModel as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Rsquared,'Rsquared')

with RsquaredModel as model:
    plotting_lib.pm.energyplot(trace_Rsquared)

Posterior predictive distribution

with RsquaredModel as model:
    posterior_pred_Rsquared = pm.sample_posterior_predictive(trace_Rsquared,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_Rsquared,posterior_pred_Rsquared,dataZ["Rsquared_z"].values,'Rsquared')

Compare prior and posterior for model parameters

with RsquaredModel as model:
    pm_data_Rsquared = az.from_pymc3(trace=trace_Rsquared,prior=prior_pred_Rsquared,posterior_predictive=posterior_pred_Rsquared)

arviz.data.io_pymc3 - WARNING - posterior predictive variable Rsquared_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,pm_data_Rsquared,'Rsquared')

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_Rsquared,'Rsquared')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_Rsquared,'Rsquared')

Asfc

with pm.Model() as model:
    AsfcModel = ThreeFactorModel('Asfc',x1,x2,x3,dataZ["Asfc_z"].values)

Verify model settings

AsfcModel.printParams(x1,x2,x3,dataZ["Asfc_z"].values)

The number of levels of the x variables are (2, 11, 139)
The standard deviations used for the beta priors are (1.0834504037573414, 1.7347208877727194, 0.46758648719539714)

pm.model_to_graphviz(AsfcModel)

Check prior choice

with AsfcModel as model:
    prior_pred_Asfc = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_Asfc,dataZ["Asfc_z"].values,'Asfc')

Prior choice is as intended: Broad over the data range.

Sampling

with AsfcModel as model:
    trace_Asfc = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=target_accept,random_seed=random_seed)
    #fit_Asfc = pm.fit(random_seed=random_seed)
    #trace_Asfc = fit_Asfc.sample(draws=numSamples)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Asfc_b3_dist, Asfc_b2_dist, Asfc_b1_dist, Asfc_b0_dist, Asfc_sigmaY, Asfc_nuY, Asfc_mu_b3, Asfc_mu_b2, Asfc_mu_b1, Asfc_mu_b0, Asfc_sigma3, Asfc_sigma2, Asfc_sigma1, Asfc_sigma0]

100.00% [8000/8000 11:08<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 668 seconds.
The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.
The estimated number of effective samples is smaller than 200 for some parameters.

with AsfcModel as model:
    if writeOut:
        with open(outPathData + 'model_{}.pkl'.format('Asfc'), 'wb') as buff:
            pickle.dump({'model': AsfcModel, 'trace': trace_Asfc}, buff)

Check sampling

with AsfcModel as model:
    dataTrace_Asfc = az.from_pymc3(trace=trace_Asfc)

pm.summary(dataTrace_Asfc,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
Asfc_mu_b0	0.05	0.83	-1.55	1.72	0.02	0.01	2909.0	2255.0	2905.0	2923.0	1.0
Asfc_mu_b1[0]	0.12	0.71	-1.35	1.45	0.01	0.01	2599.0	2599.0	2600.0	3001.0	1.0
Asfc_mu_b1[1]	-0.07	0.71	-1.55	1.28	0.01	0.01	2755.0	2673.0	2754.0	2993.0	1.0
Asfc_mu_b2[0]	1.09	0.58	0.02	2.26	0.01	0.01	1841.0	1841.0	1844.0	2312.0	1.0
Asfc_mu_b2[1]	0.87	0.55	-0.20	1.97	0.02	0.01	1376.0	1376.0	1380.0	1877.0	1.0
...	...	...	...	...	...	...	...	...	...	...	...
Asfc_mu[273]	-1.16	0.10	-1.35	-0.96	0.00	0.00	4235.0	4235.0	4229.0	3084.0	1.0
Asfc_mu[274]	-0.86	0.10	-1.06	-0.68	0.00	0.00	4135.0	4017.0	4147.0	2803.0	1.0
Asfc_mu[275]	-1.08	0.10	-1.28	-0.90	0.00	0.00	4093.0	4048.0	4115.0	2683.0	1.0
Asfc_mu[276]	-0.97	0.10	-1.16	-0.78	0.00	0.00	4176.0	4161.0	4171.0	2895.0	1.0
Asfc_mu[277]	-1.19	0.10	-1.38	-1.00	0.00	0.00	4128.0	4117.0	4124.0	2964.0	1.0

743 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Asfc,dataTrace_Asfc,'Asfc')

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with AsfcModel as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Asfc,'Asfc')

with AsfcModel as model:
    plotting_lib.pm.energyplot(trace_Asfc)

Posterior predictive distribution

with AsfcModel as model:
    posterior_pred_Asfc = pm.sample_posterior_predictive(trace_Asfc,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_Asfc,posterior_pred_Asfc,dataZ["Asfc_z"].values,'Asfc')

Compare prior and posterior for model parameters

with AsfcModel as model:
    pm_data_Asfc = az.from_pymc3(trace=trace_Asfc,prior=prior_pred_Asfc,posterior_predictive=posterior_pred_Asfc)

arviz.data.io_pymc3 - WARNING - posterior predictive variable Asfc_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,pm_data_Asfc,'Asfc')

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_Asfc,'Asfc')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_Asfc,'Asfc')

Smfc

with pm.Model() as model:
    SmfcModel = ThreeFactorModel('Smfc',x1,x2,x3,dataZ.Smfc_z.values)

Verify model settings

SmfcModel.printParams(x1,x2,x3,dataZ.Smfc_z.values)

The number of levels of the x variables are (2, 11, 139)
The standard deviations used for the beta priors are (1.2903046708375803, 3.554940942907768, 10.68509404141528)

pm.model_to_graphviz(SmfcModel)

Check prior choice

with SmfcModel as model:
    prior_pred_Smfc = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_Smfc,dataZ.Smfc_z.values,'Smfc')

Prior choice is as intended: Broad over the data range.

Sampling

with SmfcModel as model:
    trace_Smfc = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.8,random_seed=random_seed)
    #fit_Smfc = pm.fit(random_seed=random_seed)
    #trace_Smfc = fit_Smfc.sample(draws=numSamples)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Smfc_b3_dist, Smfc_b2_dist, Smfc_b1_dist, Smfc_b0_dist, Smfc_sigmaY, Smfc_nuY, Smfc_mu_b3, Smfc_mu_b2, Smfc_mu_b1, Smfc_mu_b0, Smfc_sigma3, Smfc_sigma2, Smfc_sigma1, Smfc_sigma0]

9.99% [799/8000 00:06<01:00 Sampling 4 chains, 0 divergences]

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in _mp_sample(draws, tune, step, chains, cores, chain, random_seed, start, progressbar, trace, model, callback, discard_tuned_samples, mp_ctx, pickle_backend, **kwargs)
   1485             with sampler:
-> 1486                 for draw in sampler:
   1487                     trace = traces[draw.chain - chain]

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/parallel_sampling.py in __iter__(self)
    491         while self._active:
--> 492             draw = ProcessAdapter.recv_draw(self._active)
    493             proc, is_last, draw, tuning, stats, warns = draw

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/parallel_sampling.py in recv_draw(processes, timeout)
    351         pipes = [proc._msg_pipe for proc in processes]
--> 352         ready = multiprocessing.connection.wait(pipes)
    353         if not ready:

/usr/lib/python3.7/multiprocessing/connection.py in wait(object_list, timeout)
    919             while True:
--> 920                 ready = selector.select(timeout)
    921                 if ready:

/usr/lib/python3.7/selectors.py in select(self, timeout)
    414         try:
--> 415             fd_event_list = self._selector.poll(timeout)
    416         except InterruptedError:

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

ValueError                                Traceback (most recent call last)
<ipython-input-85-755e53d074df> in <module>
      1 with SmfcModel as model:
----> 2     trace_Smfc = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.8,random_seed=random_seed)
      3     #fit_Smfc = pm.fit(random_seed=random_seed)
      4     #trace_Smfc = fit_Smfc.sample(draws=numSamples)

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in sample(draws, step, init, n_init, start, trace, chain_idx, chains, cores, tune, progressbar, model, random_seed, discard_tuned_samples, compute_convergence_checks, callback, return_inferencedata, idata_kwargs, mp_ctx, pickle_backend, **kwargs)
    543         _print_step_hierarchy(step)
    544         try:
--> 545             trace = _mp_sample(**sample_args, **parallel_args)
    546         except pickle.PickleError:
    547             _log.warning("Could not pickle model, sampling singlethreaded.")

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in _mp_sample(draws, tune, step, chains, cores, chain, random_seed, start, progressbar, trace, model, callback, discard_tuned_samples, mp_ctx, pickle_backend, **kwargs)
   1510     except KeyboardInterrupt:
   1511         if discard_tuned_samples:
-> 1512             traces, length = _choose_chains(traces, tune)
   1513         else:
   1514             traces, length = _choose_chains(traces, 0)

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in _choose_chains(traces, tune)
   1528     lengths = [max(0, len(trace) - tune) for trace in traces]
   1529     if not sum(lengths):
-> 1530         raise ValueError("Not enough samples to build a trace.")
   1531 
   1532     idxs = np.argsort(lengths)[::-1]

ValueError: Not enough samples to build a trace.

Analysis stopped here because sampling did not converge. As the plot shows, some data points are very far away from the others, which would require the analysis to be based on more heavy-tailed distributions.

HAsfc9

with pm.Model() as model:
    HAsfc9Model = ThreeFactorModel('HAsfc9',x1,x2,x3,dataZ["HAsfc9_z"].values)

Verify model settings

HAsfc9Model.printParams(x1,x2,x3,dataZ["HAsfc9_z"].values)

The number of levels of the x variables are (2, 11, 139)
The standard deviations used for the beta priors are (1.2742199511468122, 3.5115369692183998, 5.975437122957168)

pm.model_to_graphviz(HAsfc9Model)

Check prior choice

with HAsfc9Model as model:
    prior_pred_HAsfc9 = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_HAsfc9,dataZ["HAsfc9_z"].values,'HAsfc9')

Prior choice is as intended: Broad over the data range.

Sampling

with HAsfc9Model as model:
    trace_HAsfc9 = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=target_accept,random_seed=random_seed)
    #fit_HAsfc9 = pm.fit(random_seed=random_seed)
    #trace_HAsfc9 = fit_HAsfc9.sample(draws=numSamples)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [HAsfc9_b3_dist, HAsfc9_b2_dist, HAsfc9_b1_dist, HAsfc9_b0_dist, HAsfc9_sigmaY, HAsfc9_nuY, HAsfc9_mu_b3, HAsfc9_mu_b2, HAsfc9_mu_b1, HAsfc9_mu_b0, HAsfc9_sigma3, HAsfc9_sigma2, HAsfc9_sigma1, HAsfc9_sigma0]

100.00% [8000/8000 1:23:33<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 5014 seconds.
The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.
The estimated number of effective samples is smaller than 200 for some parameters.

with HAsfc9Model as model:
    if writeOut:
        with open(outPathData + 'model_{}.pkl'.format('HAsfc9'), 'wb') as buff:
            pickle.dump({'model': HAsfc9Model, 'trace': trace_HAsfc9}, buff)

Check sampling

with HAsfc9Model as model:
    dataTrace_HAsfc9 = az.from_pymc3(trace=trace_HAsfc9)

pm.summary(dataTrace_HAsfc9,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
HAsfc9_mu_b0	-0.02	0.83	-1.68	1.58	0.01	0.01	4930.0	1763.0	4905.0	3032.0	1.00
HAsfc9_mu_b1[0]	0.01	0.71	-1.38	1.45	0.01	0.01	4889.0	2383.0	4870.0	3394.0	1.00
HAsfc9_mu_b1[1]	-0.01	0.71	-1.34	1.51	0.01	0.01	4937.0	2152.0	4934.0	3077.0	1.00
HAsfc9_mu_b2[0]	-0.26	0.53	-1.37	0.74	0.01	0.01	1869.0	1869.0	1857.0	2582.0	1.00
HAsfc9_mu_b2[1]	0.07	0.52	-0.99	1.02	0.01	0.01	1892.0	1892.0	1902.0	2461.0	1.00
...	...	...	...	...	...	...	...	...	...	...	...
HAsfc9_mu[273]	0.47	0.03	0.42	0.52	0.00	0.00	3427.0	3302.0	3426.0	3592.0	1.00
HAsfc9_mu[274]	0.46	0.22	0.20	0.73	0.02	0.01	159.0	159.0	248.0	2818.0	1.01
HAsfc9_mu[275]	0.42	0.22	0.16	0.69	0.02	0.01	159.0	159.0	247.0	2869.0	1.01
HAsfc9_mu[276]	-0.09	0.02	-0.12	-0.06	0.00	0.00	3060.0	2461.0	3936.0	3005.0	1.00
HAsfc9_mu[277]	-0.13	0.02	-0.16	-0.10	0.00	0.00	3008.0	2507.0	3864.0	3304.0	1.00

743 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_HAsfc9,dataTrace_HAsfc9,'HAsfc9')

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with HAsfc9Model as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_HAsfc9,'HAsfc9')

with HAsfc9Model as model:
    plotting_lib.pm.energyplot(trace_HAsfc9)

Posterior predictive distribution

with HAsfc9Model as model:
    posterior_pred_HAsfc9 = pm.sample_posterior_predictive(trace_HAsfc9,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,prior_pred_HAsfc9,posterior_pred_HAsfc9,dataZ["HAsfc9_z"].values,'HAsfc9')

Compare prior and posterior for model parameters

with HAsfc9Model as model:
    pm_data_HAsfc9 = az.from_pymc3(trace=trace_HAsfc9,prior=prior_pred_HAsfc9,posterior_predictive=posterior_pred_HAsfc9)

arviz.data.io_pymc3 - WARNING - posterior predictive variable HAsfc9_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,pm_data_HAsfc9,'HAsfc9')

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_HAsfc9,'HAsfc9')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_HAsfc9,'HAsfc9')

Summary

The contrast plots between the two software packages are shown below again for each variable except Smfc

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_epLsar,'epLsar')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_Rsquared,'Rsquared')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_Asfc,'Asfc')

plotting_lib.plotContrast(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,x1contrast_dict,trace_HAsfc9,'HAsfc9')

Write out

!jupyter nbconvert --to html Statistical_Model_ThreeFactor_filter_weak.ipynb

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!jupyter nbconvert --to markdown Statistical_Model_ThreeFactor_filter_weak.ipynb

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